The comment was published by the British newspaper The Daily Telegraph as Romney was to arrive in London.
The presumptive Republican presidential nominee -- who begins a weeklong trip to Britain, Israel and Poland Wednesday -- is better placed to understand the "special relationship" between the United States and Britain than Obama, whose father was from Africa, the Telegraph reported Romney's adviser saying.
"We are part of an Anglo-Saxon heritage, and [Romney] feels that the special relationship is special," the aide reportedly said, adding, "The [Obama] White House didn't fully appreciate the shared history we have."
Obama's father, Barack Obama Sr., was a Kenyan senior government economist.
But Andrea Saul, Romney's press secretary, disputed the comments and emphasized that they did not reflect the beliefs of the former Massachusetts governor, CBS News reported.
"It's not true. If anyone said that, they weren't reflecting the views of Governor Romney or anyone inside the campaign," she told CBSNews.com in an e-mail.
The adviser -- one of two who spoke with the newspaper -- said Romney would abandon Obama's "left-wing" coolness toward London, The Daily Telegraph reported.
In March, Obama honored Conservative Prime Minister David Cameron with a White House state dinner, even though the queen is Britain's head of state. He took Cameron in Air Force One to a college basketball game in Dayton, Ohio, explaining the rules as the game progressed.
"One of these days I'll get my own back by getting you to a cricket match and explaining the rules to you and some of the terminology that you'll have to try and get straight, as I tried last night," Cameron said as Obama grinned the following day.
Romney's overseas tour comes four years after Obama's visit to Europe -- as a presidential hopeful ahead of the U.S. election -- attracted thousands of supporters, including 250,000 people for a landmark speech in Berlin.
Romney is to meet with Cameron Thursday.
While Cameron agrees with Romney on some issues, he also supports legalizing same-sex marriage and has called his administration the "greenest" in the nation's history.
Left-leaning British politicians chided the banks for engaging in U.S. fundraising at a time when British financial institutions face an image crisis over a scandal involving interest-rate manipulation.
Romney meets with Irish Prime Minister Enda Kenny Friday and will be present at the Summer Olympic Games' opening ceremony.
He is not expected to deliver formal remarks in Britain, his campaign said.
In Israel, Romney is expected to meet with Prime Minister Binyamin Netanyahu and other leaders.
Romney might schedule a foreign policy speech while in Poland, sources familiar with the planning told The Washington Post.